Hypotheses_Testing_p

# Hypotheses_Testing_p - Hypothesis Hypothesis Testing...

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Unformatted text preview: Hypothesis Hypothesis Testing Testing “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” … H. G. Wells Learning Objectives Understand the normal distribution and standard normal distribution. Understand what a sampling distribution is. Understand the nature and logic of hypothesis testing. Understand what a statistically significant difference is. Understand how to do hypotheses testing using SPSS. Normal Distribution First discovered by de Moivre (1667-1754) in1733 Rediscovered by Laplace (1749-1827) and also by Gauss (1777-1855) in their studies of errors in astronomical measurements. Often referred to as the Gaussian distribution. Normal (Gaussian) Distribution • Continuous, symmetric, bell-shaped curve. • Determined by two parameters, these being arithmetic mean μ and standard deviation α , N(μ, σ) . • Area under curve represents probability. 100 IQ ∞ < < ∞ =-- x e x f x- for 2 1 ) ( ) 2 /( ) ( 2 2 σ μ πσ Normal (Gaussian) Distribution Standard Normal Distribution • Also referred to as the Z distribution. • Definition: Z = (X – μ)/α (Standardizing). • When X is normally distributed, Z is N(0, 1). • Standardization allows distributions to be compared on a single scale. Normal Tables and Z-Values • Find the probability that a standard normal random variable is less than 1.35. • Locate 1.3 along the left and 0.05 along the top, and then read into the table to find the probability 0.91149. • The probability is about 0.91 that a standard normal random variable is less than 1.35. • Find the probability that a standard normal random variable is less than 0.55. • Find the probability that a standard normal random variable is between 0.55 and 1.35. Normal Tables and Z-Values • Find the standardized value corresponding to a probability of 0.75. • Locate the probability in the table that is closest to 0.75, and then reading to the left and up. • With interpolation, the required value is about 0.675. • Thus, the probability of being to the left of 0.675 under the standard normal curve is approximately 0.75. • Find the standardized value corresponding to a probability of 0.55. Normal Tables and Z-Values • Suppose X (IQ of people in HK) is normally distributed with mean 100 and standard deviation 10. Find the probability that the IQ of a randomly selected individual is less than 115. 0.93319. y probabilit the obtain to column) .00 row, (1.5 table the up Look 5 . 1 10 100 115- X Z Compute =- = = σ μ • Find the 85 th percentile of the above standard normal distribution. • How many Einsteins are there in HK (IQ > 160)?...
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Hypotheses_Testing_p - Hypothesis Hypothesis Testing...

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